If , then write the value of (x, y).

We are given that,

We need to find the value of (x, y).

Multiply the matrices on the right hand side of the equation,

For z₁₁: Dot multiply the 1^st row of first matrix and 1^st column of second matrix, then sum up.

(2 1)(1 -2) = 2 × 1 + 1 × -2

⇒ (2 1)(1 -2) = 2 – 2

⇒ (2 1)(1 -2) = 0

So,

For z₂₁: Dot multiply the 2^nd row of first matrix and 1^st column of second matrix, then sum up.

(4 3)(1 -2) = 4 × 1 + 3 × (-2)

⇒ (4 3)(1 -2) = 4 – 6

⇒ (4 3)(1 -2) = -2

So,

Equate the resulting matrix to the given matrix equation.

We know by the property of matrices,

This implies,

a₁₁ = b₁₁, a₁₂ = b₁₂, a₂₁ = b₂₁ and a₂₂ = b₂₂

Therefore,

x + y = 0

x – y = -2

Adding these two equations, we get

(x + y) + (x – y) = 0 + (-2)

⇒ x + y + x – y = -2

⇒ x + x + y – y = -2

⇒ 2x + 0 = -2

⇒ 2x = -2

⇒ x = -1

Putting x = -1 in

x + y = 0

⇒ (-1) + y = 0

⇒ -1 + y = 0

⇒ y = 1

So, putting values of x and y from above in (x, y), we get

(x, y) = (-1, 1)

Thus, (x, y) is (-1, 1).